Taxi prices are regulated because negotiation was too difficult in the pre-smartphone era and taxi drivers would take advantage of information asymmetry to screw people. None of that applies here.
The negotiation is happening between the drivers and passengers, which is how it should be. Uber and Lyft are acting as intermediaries, and are trying and failing to stop this negotiation.
Can you explain where you see a "negotiation" in this? (Don't get me wrong, I like the cut of your jib, it just seems to map better to a dysfunctional spread-based market.)
The drivers are offered a certain rate. They refuse, implicitly asking for a higher rate. This repeats until the drivers get a rate they can accept, or they give up and go home.
On the other side, passengers are offered a certain rate. They can accept it, or they can refuse and implicitly ask for a lower rate.
There's no negotiation happening, though. You don't negotiate in a bid-ask market. "I want X for $Y." "I will give X for $Y." "Done."
(And it functionally is a bid-ask market, though I'll acknowledge that it's made a bit messier by Uber and Lyft fiddling in internal-and-undocumented ways with the prices and offers that they quote.)
